The emergence of FL ushered in a new era of distributed inference that can alleviate data privacy concerns [1]}. In FL, massively distributed mobile devices and a central server (e.g., a BS) collaboratively train a shared model without requiring devices to share raw data. Many FL algorithms employ complex DNN to achieve a high accuracy by allocating many bits for the precision level in data representation [2]}. DNN structures, such as CNN, can have tens of millions of parameters and billions of MAC operations [3]}. In practice, the energy consumed for computation and memory access is proportional to the level of precision [4]}. Hence, computationally intensive neural networks with a conventional 32 bits full precision level may not be suitable for deployment on energy-constrained mobile and IoT devices. In addition, a DNN may increase the energy consumption of transmitting a training result due to the large model size. To design an energy-efficient FL scheme, one could reduce the level of precision to decrease the energy consumption for the computation and transmission. However, the reduced precision level could introduce quantization error that degrades the accuracy and the convergence rate of FL. Therefore, deploying real-world FL frameworks over wireless systems requires one to balance precision, accuracy, and energy efficiency – a major challenge facing future distributed learning frameworks.
